Theory and Modern Applications
Table 4 Temporal convergence rates for Example 3, with \(\Delta x=\Delta y=\frac{1}{160}\) and \(\nu =0.01\)
From: Numerical solution of advection–diffusion type equation by modified error correction scheme
h | t = 0.5 | t = 2.0 | ||||||
|---|---|---|---|---|---|---|---|---|
u | v | u | v | |||||
\(\mathit {err}_{R2}(t)\) | Rates | \(\mathit {err}_{R2}(t)\) | Rates | \(\mathit {err}_{R2}(t)\) | Rates | \(\mathit {err}_{R2}(t)\) | Rates | |
\(\frac{1}{80}\) | 2.50 × 10−4 | – | 1.67 × 10−4 | – | 4.28 × 10−4 | – | 2.38 × 10−4 | – |
\(\frac{1}{160}\) | 1.75 × 10−4 | 0.51 | 1.17 × 10−4 | 0.51 | 2.38 × 10−4 | 0.85 | 1.32 × 10−4 | 0.85 |
\(\frac{1}{320}\) | 9.89 × 10−7 | 7.47 | 6.61 × 10−7 | 7.47 | 8.14 × 10−7 | 8.19 | 4.53 × 10−7 | 8.19 |
\(\frac{1}{640}\) | 4.28 × 10−7 | 1.21 | 2.86 × 10−7 | 1.21 | 3.52 × 10−7 | 1.21 | 1.96 × 10−7 | 1.21 |
\(\frac{1}{1280}\) | 1.22 × 10−7 | 1.81 | 8.14 × 10−8 | 1.81 | 9.94 × 10−8 | 1.82 | 5.53 × 10−8 | 1.82 |
\(\frac{1}{2560}\) | 2.77 × 10−8 | 2.14 | 1.85 × 10−8 | 2.14 | 2.22 × 10−8 | 2.16 | 1.24 × 10−8 | 2.16 |